Finite element analysis (FEA) is a computer implemented method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
FEA is becoming increasingly popular with automobile manufacturers for optimizing both the aerodynamic performance and structural integrity of vehicles. Similarly, aircraft manufacturers rely upon FEA to predict airplane performance long before the first prototype is ever developed. One of the popular FEA tasks is to simulate an impact event such as car or truck crashworthiness. A problem associated with crashworthiness simulation is to properly simulate bolted joints or connections between two parts especially in trucks.
General purpose of a bolted joint is to clamp two or more parts together. The clamping force is achieved by applying torque to the bolt head and the nut; the mechanical advantage of the wrench and threads allows one to actually stretch the section of the bolt between the head and the nut (an area known as the grip), creating tension in the bolt. This tension is known as pretension because it exists before any other forces are applied to the joint. The pretension is transmitted to the mating parts through the head, nut, and any washers that may be present. It squeezes the mating parts together, and if the joint is designed, assembled, and maintained properly, prevents the mating parts from separating or sliding under normal loads.
Pretension needs to be simulated realistically in order to simulate bolted joints or connections properly in a finite element analysis. Many prior art approaches are cumbersome and/or tedious for users not only in creation of the FEA model, but in actual simulation itself. In one example, a prior art approach requires users to specify each bolt with a predefined axial stretch. This can be accomplished is a number of ways, for example, including the use of a thermal gradient to create the stretch or simply setting the axial stress value corresponding to the predefined stretch. Since typical FEA models may contain hundreds of bolts in close proximity, the interactions that result leave many bolts with inaccurate pretensions. During the initialization stage of a simulation, users must pay special attention to ensure that the correct pretension is indeed achieved in each and every one of the bolts in the FEA model. This prior art approach may work when there are very limited number of bolts provided these bolts are not located in substantially different orientations. In another prior art approach, each bolt is represented by a beam element, whose axial stress is iteratively determined by prescribing the motion of two beam end nodes. When the desired axial stress is reached, constraints would then be introduced and used to create a rigid link between the two beam end nodes. The primary reason for bolt pretension not reaching the desired level is due to deformation of the plates or other components within the bolted joints. In another example, a very detailed bolt model may be required (e.g., a number of solid elements) to ensure pretension as internal stress.
Therefore, it would be desirable to have an improved method of initializing bolt pretension in a finite element analysis.